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Monday, April 2, 2012

Perplexing!

I've recently had the opportunity to peruse a substantial amount of research articles about international differences in mathematics knowledge, as measured by TIMSS and PISA. I found some very interesting things in there, such as that amount of time spent on homework has a negative correlation to mathematics achievement both within and between nations. Meanwhile, frequency and effort put into homework has a positive correlation with mathematics knowledge. That's all good and great and I'm already changing how I talk to students about homework, but other results from the research studies are just bewildering:

If a student likes math, and believes in her own ability to do math, that's gotta mean the student is more likely to develop good understanding of math, right? Well, not really. Within nations, this relationship holds, and in some nations (such as Finland) the correlation is positive and quite high. But between nations, the relationship is actually the opposite: students in high-performing nations report that they like math less and consider themselves to not be good at it, compared to students in low-performing nations (Shen, 2008).

A student who is persistent with finishing tasks is likely to learn more math. That, by itself, is not weird. But Boe (2002) found that task persistance (as measured by the number of background questionnaire items answered by students in the TIMSS 1999 study) has a high correlation to mathematics achievement between nations, but less so between classrooms and very little between students. So nations in which students answered many of the background questionnaire items, which require no knowledge of mathematics or science, did better than nations in which students answered only a few of the questions. The correlation was around 0.75. On a student level, when comparing students within classrooms, the correlation was much lower. Overall, this "task persistance" variable seems to account for about 1/3 of the overall variation in results among students worldwide, and about half of the variation between nations. This is BIG. To my knowledge, no other variable has been found that explains so much of the variation. But what does it mean? Does it reflect cultural values of conscientiousness and long-term orientation (would explain why East Asian nations do so well)? Or is it that students who expect to do well on the TIMSS are more motivated to fill in the questionnaire? And WHY is the relationship strong at the nation-level but not student-level? And why, given the stunning results, has this study been cited only a handful of times since it was published 10 years ago?

One reason that Swedish researchers are interested in the TIMSS background data is that Sweden has seen a dramatic drop from acceptable to outright poor results (still better than the US, though) from TIMSS 1995 to TIMSS 2007. "Why is this happening?" we're asking. Well. Hidden among the data are little-known figures such as these: Swedish 4th-graders receive almost 30% less mathematics teaching per year than the OECD average. 8th-graders receive 20% less than OECD average. Meanwhile the Swedish media and government has aggressively blamed teachers for the poor results. To be fair, there is not a strong correlation between amount of teaching hours and mathematics knowledge. Finland, for example, ranks very high but has the fewest teaching hours of all the participating nations. US, on the other hand, has plenty of teaching hours, yet achieves very low ranking. Yet it's difficult to ignore that East Asian nations and Russia, who always top the ranks-lists, not only provide students with a LOT more teaching (South Korea for example gives students 220 teaching days each year, compared with 178 in Sweden), but also in these nations many students go to after-school mathematics tutoring.

That's it for now.

Boe, E. E., May, H., & Boruch, R. F. (2002). Student task persistence in the Third International Mathematics and
Science Study: A major source of achievement differences at the national,
classroom, and student levels (Research Rep. No. 2002-TIMSS1).
Philadelphia, PA: University of Pennsylvania, Graduate School of Education,
Center for Research and Evaluation in Social Policy.

Shen, C., & Tam, H. P. (2008). The
paradoxical relationship between student achievement and self-perception: A
cross-national analysis based on three waves of TIMSS data. Educational
Research and Evaluation, 14, 87–100.

Sue, no I gather that in Finland (within Finland) there is a moderate positive correlation between liking math and achievement. The same holds, although to a lesser extent, in most other nations. It's at a between-nation level that this correlation is reversed, so South Korean and Japanese students (for example) have higher TIMSS and PISA results but on average consider themselves not as good at math, and like it less, than US and Swedish students. I don't know how Finland compares to other nations on liking and self-concept. I did not tease it out myself, rather it's described in: Välijärvi, J., Linnakylä, J., P., Kupari, P., Reinikainen, P., & Arffman, I. (2002). The Finnish success in PISA - and some reasons behind it: PISA 2000. Jyväskylä: Institute for Educational Research, University of Jyväskylä.